Kalman PredictorThe **Kalman Predictor** indicator is a powerful tool designed for traders looking to enhance their market analysis by smoothing price data and projecting future price movements. This script implements a Kalman filter, a statistical method for noise reduction, to dynamically estimate price trends and velocity. Combined with ATR-based confidence bands, it provides actionable insights into potential price movement, while offering clear trend and momentum visualization.
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#### **Key Features**:
1. **Kalman Filter Smoothing**:
- Dynamically estimates the current price state and velocity to filter out market noise.
- Projects three future price levels (`Next Bar`, `Next +2`, `Next +3`) based on velocity.
2. **Dynamic Confidence Bands**:
- Confidence bands are calculated using ATR (Average True Range) to reflect market volatility.
- Visualizes potential price deviation from projected levels.
3. **Trend Visualization**:
- Color-coded prediction dots:
- **Green**: Indicates an upward trend (positive velocity).
- **Red**: Indicates a downward trend (negative velocity).
- Dynamically updated label displaying the current trend and velocity value.
4. **User Customization**:
- Inputs to adjust the process and measurement noise for the Kalman filter (`q` and `r`).
- Configurable ATR multiplier for confidence bands.
- Toggleable trend label with adjustable positioning.
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#### **How It Works**:
1. **Kalman Filter Core**:
- The Kalman filter continuously updates the estimated price state and velocity based on real-time price changes.
- Projections are based on the current price trend (velocity) and extend into the future (Next Bar, +2, +3).
2. **Confidence Bands**:
- Calculated using ATR to provide a dynamic range around the projected future prices.
- Indicates potential volatility and helps traders assess risk-reward scenarios.
3. **Trend Label**:
- Updates dynamically on the last bar to show:
- Current trend direction (Up/Down).
- Velocity value, providing insight into the expected magnitude of the price movement.
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#### **How to Use**:
- **Trend Analysis**:
- Observe the direction and spacing of the prediction dots relative to current candles.
- Larger spacing indicates a potential strong move, while clustering suggests consolidation.
- **Risk Management**:
- Use the confidence bands to gauge potential price volatility and set stop-loss or take-profit levels accordingly.
- **Pullback Detection**:
- Look for flattening or clustering of dots during trends as a signal of potential pullbacks or reversals.
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#### **Customizable Inputs**:
- **Kalman Filter Parameters**:
- `lookback`: Adjusts the smoothing window.
- `q`: Process noise (higher values make the filter more reactive to changes).
- `r`: Measurement noise (controls sensitivity to price deviations).
- **Confidence Bands**:
- `band_multiplier`: Multiplies ATR to define the range of confidence bands.
- **Visualization**:
- `show_label`: Option to toggle the trend label.
- `label_offset`: Adjusts the label’s distance from the price for better visibility.
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#### **Examples of Use**:
- **Scalping**: Use on lower timeframes (e.g., 1-minute, 5-minute) to detect short-term price trends and reversals.
- **Swing Trading**: Identify pullbacks or continuations on higher timeframes (e.g., 4-hour, daily) by observing the prediction dots and confidence bands.
- **Risk Assessment**: Confidence bands help visualize potential price volatility, aiding in the placement of stops and targets.
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#### **Notes for Traders**:
- The **Kalman Predictor** does not predict the future with certainty but provides a statistically informed estimate of price movement.
- Confidence bands are based on historical volatility and should be used as guidelines, not guarantees.
- Always combine this tool with other analysis techniques for optimal results.
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This script is open-source, and the Kalman filter logic has been implemented uniquely to integrate noise reduction with dynamic confidence band visualization. If you find this indicator useful, feel free to share your feedback and experiences!
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#### **Credits**:
This script was developed leveraging the statistical principles of Kalman filtering and is entirely original. It incorporates ATR for dynamic confidence band calculations to enhance trader usability and market adaptability.
Predictive
Advanced VWAP [CryptoSea]The Advanced VWAP is a comprehensive volume-weighted average price (VWAP) tool designed to provide traders with a deeper understanding of market trends through multi-layered VWAP analysis. This indicator is ideal for those who want to track price movements in relation to VWAP bands and detect key market levels with greater precision.
Key Features
Multi-Timeframe VWAP Bands: Includes multiple VWAP bands with different lookback periods (5, 10, 25, and 50), allowing traders to observe short-term and long-term price behavior.
Smoothed Band Options: Offers optional smoothing of VWAP bands to reduce noise and highlight significant trends more clearly.
Dynamic Median Line Display: Plots the median line of the VWAP bands, providing a reference for price movements and potential reversal zones.
VWAP Trend Strength Calculation: Measures the strength of the trend based on the price's position relative to the VWAP bands, normalized between -1 and 1 for easier interpretation.
In the example below we can see the VWAP Forecastd Cloud, which consists of multiple layers of VWAP bands with varying lookback periods, creating a dynamic forecast visualization. The cloud structure represents potential future price ranges by projecting VWAP-based bands outward, with darker areas indicating higher density and overlap of the bands, suggesting stronger support or resistance zones. This approach helps traders anticipate price movement and identify areas of potential consolidation or breakout as the price interacts with different layers of the forecast cloud.
How it Works
VWAP Calculation: Utilizes multiple VWAP calculations based on various lookback periods to capture a broad range of price behaviors. The indicator adapts to different market conditions by switching between short-term and long-term VWAP references.
Smoothing Algorithms: Provides the ability to smooth the VWAP bands using different moving average types (SMA, EMA, SMMA, WMA, VWMA) to suit various trading strategies and reduce market noise.
Trend Strength Analysis: Computes the trend strength based on the price's distance from the VWAP bands, with a value range of -1 to 1. This feature helps traders identify the intensity of uptrends and downtrends.
Alert Conditions: Includes alert options for crossing above or below the smoothed median line, as well as touching the smoothed upper or lower bands, providing timely notifications for potential trading opportunities.
This image below illustrates the use of smoothed VWAP bands, which provide a cleaner representation of the price's relationship to the VWAP by reducing market noise. The smoothed bands create a flowing cloud-like structure, making it easier to observe significant trends and potential reversal points. The circles highlight areas where the price interacts with the smoothed bands, indicating potential key levels for trend continuation or reversal. This setup helps traders focus on meaningful movements and filter out minor fluctuations, improving the identification of strategic entry and exit points based on smoother trend signals.
Application
Strategic Entry and Exit Points: Helps traders identify optimal entry and exit points based on the interaction with VWAP bands and trend strength readings.
Trend Confirmation: Assists in confirming trend strength by analyzing price movements relative to the VWAP bands and detecting significant breaks or touches.
Customized Analysis: Supports a wide range of trading styles by offering adjustable smoothing, band settings, and alert conditions to meet specific trading needs.
The Advanced VWAP by is a valuable addition to any trader's toolkit, offering versatile features to navigate different market scenarios with confidence. Whether used for day trading or longer-term analysis, this tool enhances decision-making by providing a robust view of price behavior relative to VWAP levels.
Session Levels Predictor [LuxAlgo]The "Session Levels Predictor" indicator predicts the maximum/minimum levels that will be made within a user-specified session. Hit rate percentages are displayed to measure how often a specific level has been hit.
🔶 USAGE
The indicator can be used to estimate the expected maximum/minimum levels within a specified session, these are directly displayed at the start of a session. This operation can be useful to set take profits/stop losses levels when we expect to exit within a specific session.
Users can display up to 3 upper and lower extremities on their chart (by default only 2 upper and lower extremities are displayed), with their distance from the session opening price being determined by the user-set percentile setting, values closer to 100 will return levels farther away from the session opening price.
Predicting maximum/minimum levels effectively allows obtaining support/resistance levels for the user-defined session, with a breakout probability indicating how easy it can be for the price to reach the estimated levels. These levels can be extended outside the specified session, allowing to test their relevancy as support/resistance levels to prices outside the specified sessions.
🔶 DETAILS
To predict maximum/minimum levels made within a session we keep a record of the distance between a session's maximum/minimum value and the session opening price (opening price when the session starts).
By using the percentile_nearest_rank() on our recorded distances we draw levels from the session opening price. If a level is hit between 2 sessions, this is saved for further calculations.
Lastly, a % hit rate of these levels is shown at the sessions open, indicating the probability that these levels could be hit before the next session.
🔹 array.percentile_nearest_rank()
Returns the value for which the specified percentage of array values (percentile) is less than or equal to it, using the nearest-rank method.
For example, taking the 75th percentile from our recorded distances between the maximum session level and session opening price will return a new distance where 75% of the recorded distances are lower.
The same goes for the green session's open - low levels
🔶 SETTINGS
Session: User-defined session interval, uses the symbol timezone.
Percentile (1, 2, 3): K-th percentile used to estimate session max/min levels, higher values will return more distant levels.
Max Population: Maximum amount of recorded distance data for the calculation of percentiles.
🔹 Style
Extend Middle Line: Toggle to extend the blue Middle Line to the next session - Default disabled
Supertrend Multiasset Correlation - vanAmsen Hello traders!
I am elated to introduce the "Supertrend Multiasset Correlation" , a groundbreaking fusion of the trusted Supertrend with multi-asset correlation insights. This approach offers traders a nuanced, multi-layered perspective of the market.
The Underlying Concept:
Ever pondered over the term Multiasset Correlation?
In the intricate tapestry of financial markets, assets do not operate in silos. Their movements are frequently intertwined, sometimes palpably so, and at other times more covertly. Understanding these correlations can unlock deeper insights into overarching market narratives and directional trends.
By melding the Supertrend with multi-asset correlations, we craft a holistic narrative. This allows traders to fathom not merely the trend of a lone asset but to appreciate its dynamics within a broader market tableau.
Strategy Insights:
At the core of this indicator is its strategic approach. For every asset, a signal is generated based on the Supertrend parameters you've configured. Subsequently, the correlation of daily price changes is assessed. The ultimate signal on the selected asset emerges from the average of the squared correlations, factoring in their direction. This indicator not only accounts for the asset under scrutiny (hence a correlation of 1) but also integrates 12 additional assets. By default, these span U.S. growth ETFs, value ETFs, sector ETFs, bonds, and gold.
Indicator Highlights:
The "Supertrend Multiasset Correlation" isn't your run-of-the-mill Supertrend adaptation. It's a bespoke concoction, tailored to arm traders with an all-encompassing view of market intricacies, fortified with robust correlation metrics.
Key Features:
- Supertrend Line : A crystal-clear visual depiction of the prevailing market trajectory.
- Multiasset Correlation : Delve into the intricate interplay of various assets and their correlation with your primary instrument.
- Interactive Correlation Table : Nestled at the top right, this table offers a succinct overview of correlation metrics.
- Predictive Insights : Leveraging correlations to proffer predictive pointers, adding another layer of conviction to your trades.
Usage Nuances:
- The bullish Supertrend line radiates in a rejuvenating green hue, indicative of potential upward swings.
- On the flip side, the bearish trajectory stands out in a striking red, signaling possible downtrends.
- A rich suite of customization tools ensures that the chart resonates with your trading ethos.
Parting Words:
While the "Supertrend Multiasset Correlation" bestows traders with a rejuvenated perspective, it's paramount to embed it within a comprehensive trading blueprint. This would include blending it with other technical tools and adhering to stringent risk management practices. And remember, before plunging into live trades, always backtest to fine-tune your strategies.
Predictive Channels [LuxAlgo]The Predictive Channels indicator is a real-time estimate of a trend channel. The indicator returns 2 resistances, 2 supports, and an average line.
🔶 USAGE
The Predictive Channels attempt to find a real-time estimate of an underlying linear trend in the price, the returned supports/resistances are constructed from this estimate.
The area between the price and the estimated trend is also highlighted, with a green color when the price is above the estimated trend, indicating a bullish variation relative to the trend, and a red color indicating a bearish variation.
Price deviating significantly from an estimated trend will return new channels. The Factor setting controls the allowed distance between the price and the trend estimate, with higher values allowing for greater distances and less frequent channels.
The Slope setting will affect the steepness of the channels, with lower values returning steeper channels, this can cause the price to more quickly deviate from the estimated trend, increasing the frequency at which new channels are created.
🔶 SETTINGS
Factor: Multiplicative factor, determines the allowed distance between the price and an estimated trend before a new channel is constructed.
Slope: Controls the line steepness of the channels, with lower values returning steeper lines.
Advanced Donchian Channels
Advanced Donchian Channels displays future donchian channel values based on the current information on the chart.
It displays a normal donchian channel at the specified user length with the future values extending from the current bar.
Depending on the direction of price movement, these values do not repaint. It is known when it does and does not repaint, and the actions are normal. See below for more information.
In a down trend, when the price is making new lows, the future "channel low" value will update every time the low is broken. The mean will also update, since the mean is the average of the channel high and channel low.
In a downtrend, the "channel high" value is concrete . It will not update until the high is broken.
Reverse these examples for uptrends.
Q;
How does it know the future values?
A:
Consider This: If we are below the current highest high, going down (aka: not setting new highs), the donchian channel "high" value will create a flat top, the flat top will start to decrease after we go further than our specified length. This is because the highest high within our specified length is no longer what it was previously. This action of time decay is a consistent movement of donchian channels . Because of this I am able to calculate these values before the current bar actually reaches them.
The indicator calculates the current length donchian channel at the current bar and then for every future bar up to your length specified it subtracts 1 from your length, calculates and displays the values accordingly.
The farthest future value is 1 length and the current bar is your specified length.
VALUES WILL ONLY BE UPDATED WHEN THE CHANNEL HIGH OR LOW IS BROKEN.
If price stays within the channel, all the future channel values will become solidified when the time reaches them.
This is not a gimmick, This data is accurate and can be used to help see future price trends
This chart should assist in visualizing what data you are seeing in this indicator.
Enjoy!
Leavitt Convolution [CC]The Leavitt Convolution indicator was created by Jay Leavitt (Stocks and Commodities Oct 2019, page 11), who is most well known for creating the Volume-Weighted Average Price indicator. This indicator is very similar to my Leavitt Projection script and I forgot to mention that both of these indicators are actually predictive moving averages. The Leavitt Convolution indicator doubles down on this idea by creating a prediction of the Leavitt Projection which is another prediction for the next bar. Obviously this means that it isn't always correct in its predictions but it does a very good job at predicting big trend changes before they happen. The recommended strategy for how to trade with these indicators is to plot a fast version and a slow version and go long when the fast version crosses over the slow version or to go short when the fast version crosses under the slow version. I have color coded the lines to turn light green for a normal buy signal or dark green for a strong buy signal and light red for a normal sell signal, and dark red for a strong sell signal.
This is another indicator in a series that I'm publishing to fulfill a special request from @ashok1961 so let me know if you ever have any special requests for me.
predictive_moving_average
Description:
Originated by John F. Ehlers, could be found within (Rocket Science for Traders, pg. 212). Aim to provide a leading indicator (I assumed for the shorter time period), which smoothed the price with no lag. The indicator derives from 2 lines crossing i.e. a weighted moving average, of higher length as a predictor and shorter length as a trigger.
Predictive Moving Average:
predict = 2*wma1 - wma2
trigger = (4*predict+3*predict +2*predict +predict)/10
Feature:
Predictive moving average
Deviation band
Notes
Consider the support/resistance (dynamic) when entering the position
Some short direction change might be identified from deviation shrink
Green indicates to enter/long, while red indicates to close/short position
[_ParkF]Mini Chart(BB)Bollinger Bands of different lengths are displayed with a line chart in front of the candle.
A Bollinger band with a length of 20 and a Bollinger band with a length of 120 can be easily identified by the circle and color displayed whenever the line passes.
In the input menu, you can edit the length and deviation of the Bollinger band, the number of candles to be displayed in front, the thickness of the line, the color, and the color of the circle.
And the expected value of each Bollinger band was measured and displayed.
You can change the thickness and color of the displayed predictive circle in Predictive of the input menu.
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서로 다른 기간값을 가진 볼린저밴드를 캔들보다 앞쪽에 선 차트와 함께 표시하였습니다.
20의 기간값을 가진 볼린저밴드와 120의 기간값을 가진 볼린저밴드를 선차트가 크로스할 때 마다 표시되는 점과 색을 통해 쉽게 식별할 수 있습니다.
input 메뉴에서 볼린저밴드의 기간값과 편차, 앞 쪽에 표시될 캔들의 수와 선의 두께, 색상, 점의 색상을 수정할 수 있습니다.
그리고 각 볼린저밴드의 예상 값을 측정하여 표시하였습니다.
input 메뉴의 Predictive에서 표시된 Predictive circle의 두께와 색상을 변경할 수 있습니다.
Ehlers Optimum Predictor [CC]The Optimum Predictor was created by John Ehlers (Rocket Science For Traders pgs 209-210) and this indicator does a pretty good job of predicting major market moves. When the blue line crosses over the red line then this indicator is predicting an upcoming uptrend and when the blue line crosses under the red line then it is predicting an upcoming downtrend. Ehlers recommends using this indicator with an entire trading system to filter out any bad signals but most of the signals it gives are pretty accurate. He uses advanced digital signal processing to predict the future prices and uses it in an ema formula for the calculation. There are several ways to interpret this indicator: you can look for crossovers, you can also look for when the indicator goes above 0 for a general uptrend or below 0 for a general downtrend.
Let me know if there are any other scripts you would like to see me publish!
Ehlers Voss Predictive Filter [CC]The Voss Predictive Filter was created by John Ehlers (Stocks and Commodities August 2019) and this is a unique indicator in that it tries to predict future price action. I have color coded the middle line to show buy and sell signals so buy when the line turns green and sell when it turns red.
Let me know if there are any other indicators you want me to publish!
[blackcat] L2 Ehlers Predictive AverageLevel: 2
Background
John F. Ehlers introuced Predictive Average in his "Rocket Science for Traders" chapter 20 on 2001.
Function
The concept of taking a difference of lagging line from the original function to produce a leading function suggests extending the concept to moving averages. There is no direct theory for this, but it seems to work pretty well. If taking a 7-bar WMA of prices, that average lags the prices by 2 bars. If taking a 7-bar WMA of the first average, this second average is delayed another 2 bars. If taking the difference between the two averages and add that difference to the first average, the result should be a smoothed line of the original price function with no lag. Sure, Dr. Ehlers tried to use more lag for the second moving average, which
should produce a better predictive curve. However, remember the lesson of Chapter 3 of the book. An analysis curve cannot precede an event. You cannot predict an event before it occurs. If then taking a 4-bar WMA of the smoothed line to create a 1-bar lag, this lagging line becomes a signal when the lines cross. This is as close to an ideal indicator as we can get.
Key Signal
Predict ---> moving average fast line
Trigger ---> moving average slow line
Pros and Cons
100% John F. Ehlers definition translation of original work, even variable names are the same. This help readers who would like to use pine to read his book. If you had read his works, then you will be quite familiar with my code style.
Remarks
The 17th script for Blackcat1402 John F. Ehlers Week publication.
Readme
In real life, I am a prolific inventor. I have successfully applied for more than 60 international and regional patents in the past 12 years. But in the past two years or so, I have tried to transfer my creativity to the development of trading strategies. Tradingview is the ideal platform for me. I am selecting and contributing some of the hundreds of scripts to publish in Tradingview community. Welcome everyone to interact with me to discuss these interesting pine scripts.
The scripts posted are categorized into 5 levels according to my efforts or manhours put into these works.
Level 1 : interesting script snippets or distinctive improvement from classic indicators or strategy. Level 1 scripts can usually appear in more complex indicators as a function module or element.
Level 2 : composite indicator/strategy. By selecting or combining several independent or dependent functions or sub indicators in proper way, the composite script exhibits a resonance phenomenon which can filter out noise or fake trading signal to enhance trading confidence level.
Level 3 : comprehensive indicator/strategy. They are simple trading systems based on my strategies. They are commonly containing several or all of entry signal, close signal, stop loss, take profit, re-entry, risk management, and position sizing techniques. Even some interesting fundamental and mass psychological aspects are incorporated.
Level 4 : script snippets or functions that do not disclose source code. Interesting element that can reveal market laws and work as raw material for indicators and strategies. If you find Level 1~2 scripts are helpful, Level 4 is a private version that took me far more efforts to develop.
Level 5 : indicator/strategy that do not disclose source code. private version of Level 3 script with my accumulated script processing skills or a large number of custom functions. I had a private function library built in past two years. Level 5 scripts use many of them to achieve private trading strategy.
Voss Predictor (A Peek Into the Future) - Dr. John EhlersI have been sitting on this for over a year, but I now present this "Voss Predictive Filter" multicator employing PSv4.0 upon initial release, originally formulated by the great and empowering Dr. John Ehlers for TASC - August 2019 Traders Tips. This is a slightly modified version of the original indicator John Ehlers designed. My improved implementation is an all-in-one combination of three indicators, consisting of Ehlers' 2-pole bandpass filter, fed into the Voss predictor, and my Correlation Color. I also purposefully attempted to make this indicator work on both "Light" and "Dark" charts equally well.
You can search for this indicator's white paper, entitled "A PEEK INTO THE FUTURE By John Ehlers", on his site in the educational reference section. It's VERY important that you fully grasp how this indicator works and when it doesn't during trending price movements. According to "TV House Rules", I can't link directly to his white paper on his web site. Technically he's a vendor, even though it has been divulged to me, that he is intending to retire after his last and final wØℾk$#Øp, where he is publicly disseminating the bulk of his unpublished proprietary code that drives his other website VERY SOON.
I love John Ehlers in a respectfully appreciative manner and he is my hero in life! I simply don't revel about pretended celebrities and supposed rock stars. I will never be able to adequately explain to you how much he has influenced me AND this website as it currently exists AND what is in store for the future of the ever evolving "Power of Pine". His inspiring legacy of code poetry shall forever be immortally enshrined here on TV and influence it.
Back to the topic of interest, this script originating from John Ehlers' mind... This indicator helps to anticipate cyclic turning points via negative group delay. It is NOT a predictive crystal ball. Do not become cluelessly disillusioned by it's title. I need to explain.
For example, this indicator could not have anticipated that the bold faced lie of "15 Days to Slow the Spread" of the CHImeravirus "plandemic" in the USA, would turn into our factual reality of multi state mandated orders demanding months of unconstitutional prison cell styled lockdowns with closures and the absurd criminalization of not wearing a mouth mask made from underwear while not being evidently ill, additionally combined with 24/7 black magick mass hypnosis spoon feeding non-scientific fear based psychological propaganda from the world's "finest" epidemiological data analysts and misleaders, eventually decimating the world's markets into zombie economies with abhorrent results of long term massive unemployment and financial hardship on a chart scale never before witnessed. Yep, it's NOT capable of predetermining any of that. I just wanted to make that very clear by example in a metaphorical manner many people can relate to concerning Voss' ability to anticipate.
The indicator consists of a bandpass filter coupled to the Voss predictor. Also, one thing about the Voss predictor, it can catch minute turning points or even false ones as explained in the white paper. So... I included my Correlation Color as a fitting companion to aid you in filtering out false signals during trending price movements. The Voss Predictive Filter should never be used alone, be forewarned!
Features List Includes:
Dark Background - Easily disabled in indicator Settings->Style for "Light" charts or with Pine commenting
AND a few more... Why list them, when you have the source code to explore!
When available time provides itself, I will consider your inquiries, thoughts, and concepts presented below in the comments section, should you have any questions or comments regarding this indicator. When my indicators achieve more prevalent use by TV members , I may implement more ideas when they present themselves as worthy additions. Have a profitable future everyone!
MultiType Shifting Predictive Moving Averages (MA) CrossoverJust 2 Moving Averages with adjustable settings and shifting capability, plus signals and predicting continuations.
At the time of publish these different types of MAs are supported:
- SMA (Simple)
- EMA (Exponential)
- DEMA (Double Exponential)
- TEMA (Triple Exponential)
- RMA (Adjusted Exponential)
- WMA (Weighted)
- VWMA (Volume Weighted)
- SWMA (Symmetrically Weighted)
- HMA (Hull)
I'm looking forward to any idea about filtering the signals. Thanks.
MultiTimeFrame Shifting Predictive Bollinger BandsThis is the optimized version of my MTFSBB indicator with capability of possible bands prediction in case of negative shifting (to the left).
Make me happy by using it and sending me your ideas about the prediction.
Ehlers Predictive Moving Average [CC]The Predictive Moving Average was created by John Ehlers (Rocket Science For Traders pg 212) and this is one of his first leading indicators. I have been asked by many people for more leading indicators so this one is for you all! Buy when the indicator line is green and sell when it is red.
Let me know if there are other indicators you would like to see me publish or if you want something custom done!
Right Sided Ricker Moving Average And The Gaussian DerivativesIn general gaussian related indicators are built by using the gaussian function in one way or another, for example a gaussian filter is built by using a truncated gaussian function as filter kernel (kernel refer to the set weights) and has many great properties, note that i say truncated because the gaussian function is not supposed to be finite. In general the gaussian function is represented by a symmetrical bell shaped curve, however the gaussian function is parametric, and the user might adjust the position of the peak as well as the width of the curve, an indicator using this parametric approach is the Arnaud Legoux moving average (ALMA) who posses a length parameter controlling the filter length, a peak parameter controlling the position of the peak of the gaussian function as well as a width parameter, those parameters can increase/decrease the lag and smoothness of the moving average output.
However what about the derivatives of the gaussian function ? We don't talk much about them and thats a pity because they are extremely interesting and have many great properties as well, therefore in this post i'll present a low lag moving average based on the modification of the 2nd order derivative of the gaussian function, i believe this post will be extremely informative and i hope you will enjoy reading it, if you are not a math person you can skip the introduction on gaussian derivatives and their properties used as filter kernel.
Gaussian Derivatives And The Ricker Wavelet
The notion of derivative is continuous, so we will stick with the term discrete derivative instead, which just refer to the rate of change in the function, we have a change function in pinescript, and we will be using it to show an approximation of the gaussian function derivatives.
Earlier i used the term 2nd order derivative, here the derivative order refer to the order of differentiation, that is the number of time we apply the change function. For example the 0 (zeroth) order derivative mean no differentiation, the 1st order derivative mean we use differentiation 1 time, that is change(f) , 2nd order mean we use differentiation 2 times, that is change(change(f)) , derivates based on multiple differentiation are called "higher derivative". It will be easier to show a graphic :
Here we can see a normal gaussian function in blue, its scaled 1st order derivative in orange, and its scaled 2nd derivative in green, note that i use scaled because i used multiplication in order for you to see each curve, else it would have been less easy to observe them. The number of time a gaussian function derivative cross 0 is based on the order of differentiation, that is 2nd order = the function crossing 0 two times.
Now we can explain what is the Ricker wavelet, the Ricker wavelet is just the normalized 2nd order derivative of a gaussian function with inverted sign, and unlike the gaussian function the only thing you can change is the width parameter. The formula of the Ricker wavelet is show'n here en.wikipedia.org , where sigma is the width parameter.
The Ricker wavelet has this look :
Because she is shaped like a sombrero the Ricker wavelet is also called "mexican hat wavelet", now what would happen if we used a Ricker wavelet as filter kernel ? The response is that we would end-up with a bandpass filter, in fact the derivatives of the gaussian function would all give the kernel of a bandpass filter, with higher order derivatives making the frequency response of the filter approximate a symmetrical gaussian function, if i recall a filter using the first order derivative of a gaussian function would give a frequency response that is left skewed, this skewness is removed when using higher order derivatives.
The Indicator
I didn't wanted to make a bandpass filter, as lately i'am more interested in low-lag filters, so how can we use the Ricker wavelet to make a low-lag low-pass filter ? The response is by taking the right side of the Ricker wavelet, and since values of the wavelets are negatives near the border we know that the filter passband is non-monotonic, that is we know that the filter will have low-lag as frequencies in the passband will be amplified.
So taking the right side of the Ricker wavelet only mean that t has to be greater than 0 and linearly increasing, thats easy, however the width parameter can be tricky to use, this was already the case with ALMA, so how can we work with it ? First it can be seen that values of width needs to be adjusted based on the filter length.
In red width = 14, in green width = 5. We can see that an higher values of width would give really low weights, when the number of negative weights is too important the filter can have a negative group delay thus becoming predictive, this simply mean that the overshoots/undershoots will be crazy wild and that a great fit will be impossible.
Here two moving averages using the previous described kernels, they don't fit the price well at all ! In order to fix this we can simply define width as a function of the filter length, therefore the parameter "Percentage Width" was introduced, and simply set the width of the Ricker wavelet as p percent of the filter length. Lower values of percent width reduce the lag of the moving average, but lets see precisely how this parameter influence the filter output :
Here the filter length is equal to 100, and the percent width is equal to 60, the fit is quite great, lower values of percent width will increase overshoots, in fact the filter become predictive once the percent width is equal or lower to 50.
Here the percent width is equal to 50. Higher values of percent width reduce the overshoots, and a value of 100 return a filter with no overshoots that is suited to act as a lagging moving average.
Above percent width is set to 100. In order to make use of the predictive side of the filter, it would be great to introduce a forecast option, however this require to find the best forecast horizon period based on length and width, this is no easy task.
Finally lets estimate a least squares moving average with the proposed moving average, you know me...a percent width set to 63 will return a relatively good estimate of the LSMA.
LSMA in green and the proposed moving in red with percent width = 63 and both length = 100.
Conclusion
A new low-lag moving average using a right sided Ricker wavelet as filter kernel has been introduced, we have also seen some properties of gaussian derivatives. You can see that lately i published more moving averages where the user can adjust certain properties of the filter kernel such as curve width for example, if you like those moving averages you can check the Parametric Corrective Linear Moving Averages indicator published last month :
I don't exclude working with pure forms of gaussian derivatives in the future, as i didn't published much oscillators lately.
Thx for reading !
Grand Trend Forecasting - A Simple And Original Approach Today we'll link time series forecasting with signal processing in order to provide an original and funny trend forecasting method, the post share lot of information, if you just want to see how to use the indicator then go to the section "Using The Indicator".
Time series forecasting is an area dealing with the prediction of future values of a series by using a specific model, the model is the main tool that is used for forecasting, and is often an expression based on a set of predictor terms and parameters, for example the linear regression (model) is a 1st order polynomial (expression) using 2 parameters and a predictor variable ax + b . Today we won't be using the linear regression nor the LSMA.
In time series analysis we can describe the time series with a model, in the case of the closing price a simple model could be as follows :
Price = Trend + Cycles + Noise
The variables of the model are the components, such model is additive since we add the component with each others, we should be familiar with each components of the model, the trend represent a simple long term variation of high amplitude, the cycles are periodic fluctuations centered around 0 of varying period and amplitude, the noise component represent shorter term irregular variations with mean 0.
As a trader we are mostly interested by the cycles and the trend, altho the cycles are relatively more technical to trade and can constitute parasitic fluctuations (think about retracements in a trend affecting your trend indicator, causing potential false signals).
If you are curious, in signal processing combining components has a specific name, "synthesis" , here we are dealing with additive synthesis, other type of synthesis are more specific to audio processing and are relatively more complex, but could be used in technical analysis.
So what to do with our components ? If we want to trade the trend, we should estimate right ? Estimating the trend component involve removing the cycle and noise component from the price, if you have read stuff about filters you should know where i'am going, yep, we should use filters, in the case of keeping the trend we can use a simple moving average of relatively high period, and here we go.
However the lag problem, which is recurrent, come back again, we end up with information easier to interpret (here the trend, which is a simple fluctuation such as a line or other smooth curve) at the cost of decision timing, that is unfortunate but as i said the information, here the moving average output, is relatively simple, and could be easily forecasted right ? If you plot a moving average of high period it would be easier for you to forecast its future values. And thats what we aim to do today, provide an estimate of the trend that should be easy to forecast, and should fit to the price relatively well in order to produce forecast that could determine the position of future closing prices observations.
Estimating And Forecasting The Trend
The parameter of the indicator dealing with the estimation of the trend is length , with higher values of length attenuating the cycle and noise component in the price, note however that high values of length can return a really long term trend unlike a simple moving average, so a small value of length, 14 for example can still produce relatively correct estimate of trend.
here length = 14.
The rough estimate of the trend is t in the code, and is an IIR filter, that is, it is based on recursion. Now i'll pass on the filter design explanation but in short, weights are constants, with higher weights allocated to the previous length values of the filter, you can see on the code that the first part of t is similar to an exponential moving average with :
t(n) = 0.9t(n-length) + 0.1*Price
However while the EMA only use the precedent value for the recursion, here we use the precedent length value, this would just output a noisy and really slow output, therefore in order to create a better fit we add : 0.9*(t(n-length) - t(n-2length)) , and this create the rough trend estimate that you can see in blue. On the parameters, 0.9 is used since it gives the best estimate in my opinion, higher values would create more periodic output and lower values would just create a rougher output.
The blue line still contain a residual of the cycle/noise component, this is why it is smoothed with a simple moving average of period length. If you are curious, a filter estimating the trend but still containing noisy fluctuations is called "Notch" filter, such filter would depending on the cutoff remove/attenuate mid term cyclic fluctuations while preserving the trend and the noise, its the opposite of a bandpass filter.
In order to forecast values, we simply sum our trend estimate with the trend estimate change with period equal to the forecasting horizon period, this is a really really simple forecasting method, but it can produce decent results, it can also allows the forecast to start from the last point of the trend estimate.
Using The Indicator
We explained the length parameter in the precedent section, src is the input series which the trend is estimated, forecast determine the forecasting horizon, recommend values for forecast should be equal to length, length/2 or length*2, altho i strongly recommend length.
here length and forecast are both equal to 14 .
The corrective parameter affect the trend estimate, it reduce the overshoot and can led to a curve that might fit better to the price.
The indicator with the non corrective version above, and the corrective one below.
The source parameter determine the source of the forecast, when "Noisy" is selected the source is the blue line, and produce a noisy forecast, when "Smooth" is selected the source is the moving average of t , this create a smoother forecast.
The width interval control...the width of the intervals, they can be seen above and under the forecast plot, they are constructed by adding/subtracting the forecast with the forecast moving average absolute error with respect to the price. Prediction intervals are often associated with a probability (determining the probability of future values being between the interval) here we can't determine such probability with accuracy, this require (i think) an analysis of the forecasting distribution as well as assumptions on the distribution of the forecasting error.
Finally it is possible to see historical forecasts, that is, forecasts previously generated by checking the "Show Historical Forecasts" option.
Examples
Good forecasts mostly occur when the price is close to the trend estimate, this include the following highlighted periods on AMD 15TF with default settings :
We can see the same thing at the end of EURUSD :
However we can't always obtain suitable fits, here it is isn't sufficient on BTCUSD :
We can see wide intervals, we could change length or use the corrective option to get better results, another option is to use a log scale.
We will end the examples with the log SPX, who posses a linear trend, so for example a linear model such as a linear regression would be really adapted, lets see how the indicator perform :
Not a great fit, we could try to use an higher length value and use "Smooth" :
Most recent fits are quite decent.
Conclusions
A forecasting indicator has been presented in this post. The indicator use an original approach toward estimating the trend component in the closing price. Of course i should have given statistics related to the forecasting error, however such analysis is worth doing with better methods and in more advanced environment allowing for optimization.
But we have learned some stuff related to signal processing as well as time series analysis, seeing a time series as the sum of various components is really helpful when it comes to make sense of chaotic and noisy series and is a basic topic in time series analysis.
You can see that in this new year i work harder on the visual of my indicators without trying to fall in the label addict trap, something that i wasn't really doing before, let me know what do you think of it.
Thanks for reading !
Recursive RsiIntroduction
I have already posted a classic indicator using recursion, it was the stochastic oscillator and recursion helped to get a more predictive and smooth result. Here i will do the same thing with the rsi oscillator but with a different approach. As reminder when using recursion you just use a fraction of the output of a function as input of the same function, i say a fraction because if you feedback the entire output you will just have a periodic function, this is why you average the output with the input.
The Indicator
The indicator will use 50% of the output and 50% of the input, remember that when using feedback always rescale your input, else the effect might be different depending on the market you are in. You can interpret the indicator like a normal rsi except if you plan to use the 80/20 level, depending on length the scale might change, if you need a fixed scale you can always rescale b by using an rsi or stochastic oscillator.
Conclusion
I have presented an rsi oscillator using a different type of recursion structure than the recursive stochastic i posted in the past, the result might be more predictive than the original rsi. Hope you like it and thanks for reading !
Linear Quadratic Convergence Divergence OscillatorIntroduction
I inspired myself from the MACD to present a different oscillator aiming to show more reactive/predictive information. The MACD originally show the relationship between two moving averages by subtracting one of fast period and another one of slow period. In my indicator i will use a similar concept, i will subtract a quadratic least squares moving average with a linear least squares moving average of same period, since the quadratic least squares moving average is faster than the linear one and both methods have low-lag this will result in a reactive oscillator.
LQCD In Details
A quadratic least squares moving average try to fit a quadratic function (parabola) to the price by using the method of least squares, the linear least squares moving average try to fit a line. Non-linear fit tend to minimize the sum of squares in non-linear data, this is why a quadratic method is more reactive. The difference of both filters give us an oscillator, then we apply a simple moving average to this oscillator to provide the signal line, subtracting the oscillator and its signal line give us the histogram, those two last steps are the same used in the MACD.
Length control the period of the quadratic/linear moving average. While the MACD use a signal line for plotting the histogram i also added the option to plot the momentum of the quadratic moving average instead, the result is smoother and reduce irregularities, in order to do so just check the differential option in the parameter box.
The period of the signal line and the momentum are both controlled by the signal parameter.
A predictive approach can be made by subtracting the histogram with the signal line, this process make the histogram way more predictive, in order to do so just check the predictive histogram option in the parameter box.
Predictive histogram with simple histogram option. The differential mode can also be used with the predictive parameter, this result in a smoother but less reactive prediction.
Information Interpretation
The amount of information the MACD can give us is high. We can use the histogram as signal generator, or the if the oscillator is over/under 0, combine the oscillator/signal line with histogram, combinations can provide various systems. Some traders use the histogram as signal generator and use the cross between the histogram and the signal line as a stop signal, this method can avoid some whipsaw trades. The study of divergences with the price is also another method.
Conclusion
This oscillator aim to show the same amount of information as the MACD with a similar calculation method but using different kind of filters as well as eliminating the need to use two separates periods for the moving averages calculation, its still possible to use different periods for the quadratic/linear moving average but the results can be less accurate. This indicator can be used like the MACD.
Dominant Cycle Tuned Rsi BackgroundBackground version of the Dominant Cycle Tuned Rsi Background published here
Dominant Cycle Tuned RsiIntroduction
Adaptive technical indicators are importants in a non stationary market, the ability to adapt to a situation can boost the efficiency of your strategy. A lot of methods have been proposed to make technical indicators "smarters" , from the use of variable smoothing constant for exponential smoothing to artificial intelligence.
The dominant cycle tuned rsi depend on the dominant cycle period of the market, such method allow the rsi to return accurate peaks and valleys levels. This indicator is an estimation of the cycle finder tuned rsi proposed by Lars von Thienen published in Decoding the Hidden Market Rhythm/Fine-tuning technical indicators using the dominant market vibration/2010 using the cycle measurement method described by John F.Ehlers in Cybernetic Analysis for Stocks and Futures .
The following section is for information purpose only, it can be technical so you can skip directly to the The Indicator section.
Frequency Estimation and Maximum Entropy Spectral Analysis
“Looks like rain,” said Tom precipitously.
Tom would have been a great weather forecaster, but market patterns are more complex than weather ones. The ability to measure dominant cycles in a complex signal is hard, also a method able to estimate it really fast add even more challenge to the task. First lets talk about the term dominant cycle , signals can be decomposed in a sum of various sine waves of different frequencies and amplitudes, the dominant cycle is considered to be the frequency of the sine wave with the highest amplitude. In general the highest frequencies are those who form the trend (often called fundamentals) , so detrending is used to eliminate those frequencies in order to keep only mid/mid - highs ones.
A lot of methods have been introduced but not that many target market price, Lars von Thienen proposed a method relying on the following processing chain :
Lars von Thienen Method = Input -> Filtering and Detrending -> Discrete Fourier Transform of the result -> Selection using Bartels statistical test -> Output
Thienen said that his method is better than the one proposed by Elhers. The method from Elhers called MESA was originally developed to interpret seismographic information. This method in short involve the estimation of the phase using low amount of information which divided by 360 return the frequency. At first sight there are no relations with the Maximum entropy spectral estimation proposed by Burg J.P. (1967). Maximum Entropy Spectral Analysis. Proceedings of 37th Meeting, Society of Exploration Geophysics, Oklahoma City.
You may also notice that these methods are plotted in the time domain where more classic method such as : power spectrum, spectrogram or FFT are not. The method from Elhers is the one used to tune our rsi.
The Indicator
Our indicator use the dominant cycle frequency to calculate the period of the rsi thus producing an adaptive rsi . When our adaptive rsi cross under 70, price might start a downtrend, else when our adaptive rsi crossover 30, price might start an uptrend. The alpha parameter is a parameter set to be always lower than 1 and greater than 0. Lower values of alpha minimize the number of detected peaks/valleys while higher ones increase the number of those. 0.07 for alpha seems like a great parameter but it can sometimes need to be changed.
The adaptive indicator can also detect small top/bottoms of small periods
Of course the indicator is subject to failures
At the end it is totally dependent of the dominant cycle estimation, which is still a rough method subject to uncertainty.
Conclusion
Tuning your indicator is a great way to make it adapt to the market, but its also a complex way to do so and i'm not that convinced about the complexity/result ratio. The version using chart background will be published separately.
Feel free to tune your indicators with the estimator from elhers and see if it provide a great enhancement :)
Thanks for reading !
References
for the calculation of the dominant cycle estimator originally from www.davenewberg.com
Decoding the Hidden Market Rhythm (2010) Lars von Thienen
Ehlers , J. F. 2004 . Cybernetic Analysis for Stocks and Futures: Cutting-Edge DSP Technology to Improve Your Trading . Wiley
